Temporal non-equilibrium dynamics of a Bose Josephson junction in presence of incoherent excitations

TL;DR

This paper develops a non-equilibrium Green's function method to study the dynamics of a Bose-Einstein condensate in a double-well trap, revealing a transition from Josephson to Rabi oscillations influenced by trap parameters.

Contribution

It introduces a detailed Green's function approach to analyze coupled condensate and excitation dynamics in a trap, highlighting a transition time scale in non-equilibrium behavior.

Findings

Undamped Josephson oscillations for t<τ_c

Transition to fast Rabi oscillations at τ_c

Dependence of τ_c on trap frequency Δ

Abstract

The time-dependent non-equilibrium dynamics of a Bose-Einstein condensate (BEC) typically generates incoherent excitations out of the condensate due to the finite frequencies present in the time evolution. We present a detailed derivation of a general non-equilibrium Green's function technique which describes the coupled time evolution of an interacting BEC and its single-particle excitations in a trap, based on an expansion in terms of the exact eigenstates of the trap potential. We analyze the dynamics of a Bose system in a small double-well potential with initially all particles in the condensate. When the trap frequency is larger than the Josephson frequency, $\Delta > \omega_J$, the dynamics changes at a characteristic time $\tau_c$ abruptly from slow Josephson oscillations of the BEC to fast Rabi oscillations driven by quasiparticle excitations in the trap. For times $t<\tau_c$ the Josephson oscillations are undamped, in agreement with experiments. We analyze the physical origin of the finite scale $\tau_c$ as well as its dependence on the trap parameter $\Delta$.